Rival agency Standard and Poor's added: "Washington's governance and policymaking had become less stable."

S&P added that the deal had done nothing to put the finances of the US on a more sustainable footing.

The deficit has topped $1tn in each of the past four years.

Moody's said that if the US failed to cut the deficit, the government's top credit rating could be at risk.

'Less stable'

The fiscal cliff measures - $536bn of tax rises and $109bn of spending cuts - had been due to come into effect at midnight on Monday, but Congress agreed a deal to avoid the worst of the measures late on Tuesday.

Shares across the world rallied on Wednesday in response to the deal. That boost was not sustained, however, with most European markets trading lower on Thursday.

The deal postponed the hardest decisions that Republican and Democratic politicians must agree on - spending cuts.

Moody's said the outcome of these negotiations about spending levels would determine whether it downgraded US government debt, a move which could in theory make it more expensive for the government to borrow, further damaging its finances.

The measures finally agreed during late night talks between Republicans and Democrats included:

Tax increases and limits on exemptions and deductions for higher earners

Higher inheritance tax for the largest estates

A one-year extension for unemployment benefits, affecting two million people

A five-year extension for tax credits that help poorer and middle-class families

The US Congressional Budget Office, the independent body which analyses the effect of government decisions on the US economy, said the measures would add $4tn to US budget deficits over the next decade.

Fiscal cliff explained

On 1 January 2013, tax increases and huge spending cuts were due to come into force - the so-called fiscal cliff

The deadline was put in place in 2011 to force the president and Congress to agree ways to save money over the next 10 years

The fear was that raising taxes while massively cutting spending would have huge impact on households and businesses

Experts believed it could have pushed the US into recession, and had a global impact on growth

A deal has been reached delaying some of the tax rises and all of the spending cuts by at least two months

This projected increase means that an agreement on cuts is crucial if the government is to bring down the deficit - the shortfall between what a government spends and what it gets back through the likes of tax revenue.

Although more tax revenue should be raised from the agreement to impose a higher tax rate on those earning over $400,00 a year, that will be more than outweighed by the loss of revenue from extending tax breaks to lower earners, Moody's said.

It also pointed out that the deal was welcome in that it averted the recession that would have occurred if all of the fiscal cliff measures had been allowed to have come in.

But it warned that threats to economic growth remained as rises in payroll taxes that came into effect at the start of the year could hit the amount consumers spend.

Standard and Poor's had a similar view of the outlook for the US economy, saying the "fiscal cloud" hanging over it had only partially been lifted.

Spending cuts, depending on how deep they are and where they are made, could also have a detrimental impact on growth and hence government finances, the credit agencies said.

'No tough stuff'

Following the deal to avoid the fiscal cliff, the chairman of a bi-partisan commission to look at lowering the deficit, Erskine Bowles, said: "They didn't do any of the tough stuff. We've taken two steps now, but those two steps combined aren't enough to put our fiscal house in order."

The fiscal cliff deal also did nothing to tackle the issue of the debt ceiling - the legal limit on how much the country can borrow - Moody's pointed out, and this will have to be tackled in February or early March.

The total amount the government can borrow is currently set at $16.4tn and the government is set to run out of money in the next two months if this limit is not raised by Congress.

Both are expected to be discussed in the coming weeks. The fact that the negotiations about spending and the debt ceiling could come at the same time, raises the prospect of further damaging political brinkmanship, S&P warned.

Republicans are pushing for bigger spending cuts than the Democrats have so far been willing to accept.

During the last stalemate over the debt ceiling in the summer of 2011, S&P downgraded the country's top-notch AAA credit rating to AA+ for the first time.

S&P said at the time that governance and policymaking in the US had become, "less stable, less effective and less predictable".

"We believe that this characterisation still holds," it said.

* The payroll tax was cut by 2% two years ago to stimulate the economy ** The federal Emergency Unemployment Compensation program, which pays recipients while they search for a job, was due to end *** The “doc fix” is short term funding for Medicare providers to ensure salaries remain stable